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Heat conduction
Heat conduction is the transmission of heat across matter. Heat transfer is always directed from a higher to a lower temperature. Denser http://en.wikipedia.org/wiki/Density substances are usually better conductors; metals are excellent conductors. The law of heat conduction also know as Fourier's law states that the time rate of heat flow Q'' through a slab (or a portion of a perfectly insulated wire, as shown in the figure) is proportional http://en.wikipedia.org/wiki/Proportional to the gradient http://en.wikipedia.org/wiki/Gradient of temperature difference: : Q = k A \frac{\Delta T}{\Delta x} ''A is the transversal surface area, \Delta x is the thickness of the body of matter through which the heat is passing, k'' is a conductivity constant dependent on the nature of the material and its temperature, and \Delta T is the temperature difference through which the heat is being transferred. This law forms the basis for the derivation of the heat equation http://en.wikipedia.org/wiki/Heat_equation. R-value http://en.wikipedia.org/wiki/R-value is the unit for heat resistance, the reciprocal of the conductance. Ohm's law is the electrical analogue of ''Fourier's law. Conductance Writing : U = \frac{k}{\Delta x}, \quad Fourier's law can also be stated as: : Q = U A\, \Delta T \quad where U'' is the conductance. The reciprocal of conductance is resistance, equal to: : \frac{A\, \Delta T}{Q}, \quad and it is resistance which is additive when several conducting layers lie between the hot and cool regions, because ''A and Q'' are the same for all layers. In a multilayer partition, the total conductance is related to the conductance of its layers by: : \frac{1}{U} = \frac{1}{U_1} + \frac{1}{U_2} + \frac{1}{U_3}+ \cdots So, when dealing with a multilayer partition, the following formula is usually used: : Q = \frac{A\,\Delta T}{\frac{\Delta_1 x}{K_1} + \frac{\Delta_2 x}{K_2} + \frac{\Delta_3 x}{K_3}+ \cdots} When heat is being conducted from one fluid to another through a barrier, it is sometimes important to consider the conductance of the thin film of fluid which remains stationary next to the barrier. This thin film of fluid is difficult to quantify, its characteristics depending upon complex conditions of turbulence and viscosity, but when dealing with thin high-conductance barriers it can sometimes be quite significant. Newton's law of cooling A related principle, '''Newton's law of cooling', states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. This form of heat loss principle, however, is not very precise; a more accurate formulation requires an analysis of heat flow based on the heat equation in an inhomogeneous medium. The general applicability of this simplification is characterized by the Biot number http://en.wikipedia.org/wiki/Biot_number. Nevertheless, it is easy to derive from this principle the exponential decay http://en.wikipedia.org/wiki/Exponential_decay of temperature of a body. If T'' is the temperature of the body, then : \frac{d T(t)}{d t} = - r (T - T_{\mathrm{env}}) where ''r is some positive constant. From which, it follows that : T(t) = T_{\mathrm{env}} + (T(0) - T_{\mathrm{env}}) \ e^{-r t}. \quad For example, simplified climate models http://en.wikipedia.org/wiki/Climate_model may use Newtonian cooling instead of a full (and computationally expensive) radiation code to maintain atmospheric temperatures. See also * Heat * Mpemba effect http://en.wikipedia.org/wiki/Mpemba_effect * Scientific laws named after people * Thermal conductivity http://en.wikipedia.org/wiki/Thermal_conductivity * Convection http://engineering.wikicities.com/wiki/Special:Search?search=Convection&go=Go * Thermal radiation http://en.wikipedia.org/wiki/Thermal_radiation * Heatpipe Category:Mechanical engineering Category:Heat exchangers Category:Energy Category:Electronics